Download Polynomials Formative Practice.tst

Polynomials Formative Practice
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) The length of a rectangle is three inches more than the width. The area of the rectangle is 154 inches. Find the
width of the rectangle.
A) 14 inches
B) 6 inches
C) 11 inches
D) 7 inches
2) The area of a square is numerically 4 less than the perimeter. Find the length of the side, if the side is greater
than 1.
A) 5 units
B) 8 units
C) 2 units
D) 9 units
Find the vertex of the parabola.
3) f(x) = 3x2 + 30x - 5
A) (-3, -5)
B) (3, 5)
C) (-5, -80)
D) (5, 3)
4) f(x) = x2 - 14x + 54
A) (5, 7)
B) (7, 5)
C) (0, 7)
D) (5, 0)
Determine whether there is a maximum or minimum value for the given function, and find that value.
5) f(x) = x2 + 8x + 8
A) Maximum: -8
B) Minimum: -8
C) Minimum: -4
D) Maximum: 0
Solve.
6) The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches,
according to the equation M(x) = 10x - x2 . What rainfall produces the maximum number of mosquitoes?
A) 10 in.
B) 0 in.
C) 5 in.
D) 100 in.
Find the correct end behavior diagram for the given polynomial function.
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7) P(x) = x7 + 2x2 - 1
3
A)
B)
C)
Use substitution to determine whether the given number is a zero of the given polynomial.
8) -1; P(x) = x4 + 9x2 - 10
A) Yes
B) No
Find the zeros of the polynomial function and state the multiplicity of each.
9) f(x) = -5x2 (x - 8)(x + 2)3
A) -2, multiplicity 1; 2, multiplicity 1; 8, multiplicity 1
B) -2, multiplicity 3; 0, multiplicity 2; 8, multiplicity 1
C) -2, multiplicity 3; 8, multiplicity 1
D) -2, multiplicity 3; 0, multiplicity 2; 2, multiplicity 1; 8, multiplicity 1
Graph the function.
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D)
10) P(x) = (3x - 2)(x + 2)2
10
y
5
-10
-5
x
5
-5
-10
A)
B)
10
y
10
5
-10
y
5
-5
5
x
-10
-5
-5
-5
-10
-10
C)
5
x
5
x
D)
10
y
10
5
-10
-5
y
5
5
x
-10
-5
-5
-5
-10
-10
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Evaluate the function for the given values of a and b. Then use the intermediate value theorem to determine which of
the statements below is true.
11) a = -2 and b = -1
P(x) = 10x3 - 10x + 3
A) P(-2) and P(-1) have the same sign, therefore the intermediate value theorem cannot be used to
determine whether P has a real zero between -2 and -1.
B) P(-2) and P(-1) have opposite signs, therefore P does not have a real zero between -2 and -1.
C) P(-2) and P(-1) have opposite signs, therefore P has a real zero between -2 and -1.
D) P(-2) and P(-1) have the same sign, therefore P does not have a real zero between -2 and -1.
Use synthetic division to find the quotient and the remainder.
12) (3x 4 - 9x 3 + 2x 2 - 6x) ÷ (x - 3)
A) Q(x) = (3x3 - 2x); R(x) = 0
C) Q(x) = (3x3 + x2 - x + 3); R(x) = 9
B) Q(x) = (3x3 + 2x); R(x) = 0
D) Q(x) = (3x2 + 2x); R(x) = 0
Using synthetic division, determine whether the numbers are zeros of the polynomial.
13) 7, 2; f(x) = x3 - 10x2 + 28x - 24
A) Yes; yes
B) No; no
C) No; yes
D) Yes; no
Factor the polynomial f(x). Then solve the equation f(x) = 0.
14) f(x) = x3 - 11x2 + 36x - 36
A) (x - 2)(x - 3)(x - 7) ; 2, 3, 7
C) (x + 2)(x - 3)(x + 6) ; -2, 3, -6
B) (x - 2)(x + 3)(x - 6) ; -2, 3, -6
D) (x - 2)(x - 3)(x - 6) ; 2, 3, 6
15) f(x) = x4 - 8x3 + 17x2 + 2x - 24
A) (x - 1)(x + 2)(x + 3)(x + 4); 1, -2, -3, -4
C) (x + 1)(x - 2)(x - 3)(x - 4); -1, 2, 3, 4
B) (x + 1)(x + 2)(x + 3)(x - 4); -1, -2, -3, 4
D) (x - 1)(x - 2)(x - 3)(x - 4); 1, 2, 3, 4
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Graph the polynomial function. Use synthetic division and the remainder theorem to find the zeros.
16) f(x) = x3 + 4x2 - 3x - 18
60
y
6 x
-6
-60
B) -2 (multiplicity 2), 2;
A) 3 (multiplicity 2), 2;
60
y
60
6 x
-6
y
6 x
-6
-60
-60
C) -3, 3, 2;
D) -3 (multiplicity 2), 2;
60
y
60
6 x
-6
y
6 x
-6
-60
-60
Find the requested polynomial.
17) Find a polynomial function of degree 3 with 4, i, -i as zeros.
A) f(x) = x3 - 4x2 + x - 4
B) f(x) = x3 + 4x2 - x + 4
C) f(x) = x3 - 4ix2 + x - 4i
D) f(x) = x3 - 4x2 + ix - 4i
18) Find a polynomial of degree 3 having the following zeros:
1 + 2 , 1 - 2 , and 7
A) f(x) = x3 + 9x2 - 13x + 7
C) f(x) = x3 - 10x2 + 14x - 7
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B) f(x) = x3 - 9x2 + 13x + 7
D) f(x) = x3 - 9x2 + 13x - 7
Provide the requested response.
19) Suppose that a polynomial function of degree 6 with rational coefficients has 2i, -2 + 3i, 3 - 3 as zeros. Find
the other zeros.
A) -2i, 2 - 3i , -3 + 3
B) 2 - 3i , -3 + 3
C) -2i, -2 - 3i , 3 + 3
D) -2 - 3i , 3 + 3
Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros.
20) -4i, 2
A) f(x) = x4 - 12x2 + 64
B) f(x) = x3 - 3x2 + 16x + 32
D) f(x) = x3 - 2x2 + 16x - 32
C) f(x) = x4 + 12x2 - 64
Given the polynomial function f(x), find the rational zeros, then the other zeros (that is, solve the equation f(x) = 0), and
factor f(x) into linear factors.
21) f(x) = x3 - 6x2 + 6x + 8
A) 4, -1 + 3 , -1 - 3 ; f(x) = (x - 4)(x + 1 - 3)(x + 1 + 3)
B) -4, 1 + 3 , 1 - 3 ; f(x) = (x + 4)(x - 1 - 3)(x - 1 + 3)
C) 4, 1 + 3 , 1 - 3 ; f(x) = (x - 4)(x + 1 - 3)(x + 1 + 3)
D) 4, 1 + 3 , 1 - 3 ; f(x) = (x - 4)(x - 1 - 3)(x - 1 + 3)
22) f(x) = x3 - 64
A) 4, -2 + 2
B) 4, -2 + 2
C) 4, 2 + 2
D) 4, -2 + 3 , -2 - 2 3 ; f(x) = (x - 4) (x + 2 - 2 3 )(x + 2 + 2 3 )
3 i, -2 - 2 3 i ; f(x) = (x - 4) (x + 2 - 2 3 i)(x + 2 + 2 3 i)
3 i, 2 - 2 3 i ; f(x) = (x - 4) (x - 2 - 2 3 i)(x - 2 + 2 3 i)
3 i, -2 - 3 i ; f(x) = (x - 4) (x + 2 - 3 i)(x + 2 + 3 i)
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Answer Key
Testname: POLYNOMIALS FORMATIVE PRACTICE
1) C
2) C
3) C
4) B
5) B
6) C
7) D
8) A
9) B
10) C
11) C
12) B
13) C
14) D
15) C
16) D
17) A
18) B
19) C
20) D
21) D
22) B
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